![]() Additionally, the algorithm requires substantial communication between processing threads and plenty of memory bandwidth. The parallel FFT algorithm is designed to "divide and conquer" so that a similar task is performed repeatedly on different data. Each time step requires two FFTs and four IFFTs on different matrices, and a single computation can involve hundreds of thousands of time steps. The exact number depends on the size of the grid (Figure 2) and the number of time steps included in the simulation. The algorithm performs many fast Fourier transforms (FFTs) and inverse fast Fourier transforms (IFFTs). Wave equations are used in a wide range of engineering disciplines, including seismology, fluid dynamics, acoustics, and electromagnetics, to describe sound, light, and fluid waves.Īn algorithm that uses spectral methods to solve wave equations is a good candidate for parallelization because it meets both of the criteria for acceleration using the GPU (see "Will Execution on a GPU Accelerate My Application?"): We illustrate this approach by solving a second-order wave equation using spectral methods. This article demonstrates features in Parallel Computing Toolbox ™ that enable you to run your MATLAB ® code on a GPU by making a few simple changes to your code. ![]() Additionally, you must spend time fine-tuning your code for your specific GPU to optimize your applications for peak performance. Second, programming for GPUs in C or Fortran requires a different mental model and a skill set that can be difficult and time-consuming to acquire. 1 This means that your overall computational speedup is limited by the amount of data transfer that occurs in your algorithm. Because a GPU is attached to the host CPU via the PCI Express bus, the memory access is slower than with a traditional CPU. Data must be sent from the CPU to the GPU before calculation and then retrieved from it afterwards. First, memory access becomes a much more likely bottleneck for your calculations. It makes efficient use of memory caches.The greatly increased throughput made possible by a GPU, however, comes at a cost.This approach is suitable for multiprocessing systems.This approach also simplifies other problems, such as the Tower of Hanoi. Strassen's matrix multiplication) is O(n 2.8074). The complexity for the multiplication of two matrices using the naive method is O(n 3), whereas using the divide and conquer approach (i.e.In a dynamic approach, mem stores the result of each subproblem.Īdvantages of Divide and Conquer Algorithm Suppose we are trying to find the Fibonacci series. Use the dynamic approach when the result of a subproblem is to be used multiple times in the future. Use the divide and conquer approach when the same subproblem is not solved multiple times. The result of each subproblem is not stored for future reference, whereas, in a dynamic approach, the result of each subproblem is stored for future reference. The divide and conquer approach divides a problem into smaller subproblems these subproblems are further solved recursively. T(n/2) = O(n log n) (To understand this, please refer to the master theorem.) N/b = n/2 (size of each sub problem is half of the input)į(n) = time taken to divide the problem and merging the subproblems Let us take an example to find the time complexity of a recursive problem.įor a merge sort, the equation can be written as:Ī = 2 (each time, a problem is divided into 2 subproblems) All subproblems are assumed to have the same size.į(n) = cost of the work done outside the recursive call, which includes the cost of dividing the problem and cost of merging the solutions The complexity of the divide and conquer algorithm is calculated using the master theorem.Ī = number of subproblems in the recursion Here, conquer and combine steps go side by side. Now, combine the individual elements in a sorted manner. ![]() merge sort).Īgain, divide each subpart recursively into two halves until you get individual elements. Here, we will sort an array using the divide and conquer approach (ie. Let us understand this concept with the help of an example.
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